Question

In: Statistics and Probability

(b) In a new casino game, two balls are chosen randomly from an urn containing 8...

(b) In a new casino game, two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls to see if you will win any money. Suppose that you win $2 for each black ball selected, you lose $1 for each white ball selected, and you get nothing for each orange ball selected. If the casino lets you play this new casino game with no entry fee, what is the probability that you will not lose any money? [7 marks]

(c) A survey was conducted on lawyers at two different law firms about their annual incomes. The following table displays data for the 275 lawyers who responded to the survey.

ANNUAL INCOME

LAW FIRM 1

LAW FIRM 2

TOTAL

UNDER $45000

$45000 TO $89999

$90000 AND OVER

30

35

100

20

40

50

75

150

TOTAL

165

110

275

(d) A smartphone company receives shipments of smartphones from three factories, labelled, 1, 2 and 3. Twenty-five percent of shipments come from factory 1 whose shipments contain 8% defective smartphones. Sixty-five percent of the shipments come from factory 2 whose shipments contain 6% defective smartphones. The remainder of the shipments comes from factory 3 whose shipments contain 4% smartphones. The company receives a shipment, but does not know the source. A random sample of 15 smartphones is inspected, and three of the smartphones are found to be defective. What is the probability that this shipment came from factory 2?

Expert Solution

b) ANSWER

C)

What you have to calculated, The question is not provided.

D)

orchestra answered 2 years ago

Q2. Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2...

Q2. Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected. Let X denote our winnings. What are the possible values of X, and what are the probabilities associated with each value i.e. create a discrete probability distribution table for winning amount. Compute the expected value of winnings and standard deviation of winnings. You...

Two balls are chosen randomly from a box containing 8 white, 4 red, and 2 green...

Two balls are chosen randomly from a box containing 8 white, 4 red, and 2 green balls to see if you will win any money. Suppose that you win $2 for each red ball selected, you lose $1 for each blue ball selected, and you get nothing for each green ball selected. What is the probability that you will not lose any money?

An urn contains 6 red balls and 4 green balls. Three balls are chosen randomly from...

An urn contains 6 red balls and 4 green balls. Three balls are chosen randomly from the urn, without replacement. (a) What is the probability that all three balls are red? (Round your answer to four decimal places.) (b) Suppose that you win $20 for each red ball drawn and you lose $10 for each green ball drawn. Compute the expected value of your winnings.

In a certain lottery, an urn contains balls numbered 1 to 34. From this urn, 4 balls are chosen randomly, without replacement

In a certain lottery, an urn contains balls numbered 1 to 34. From this urn, 4 balls are chosen randomly, without replacement. For a $1 bet, a player chooses one set of four numbers. To win, all four numbers must match those chosen from the urn. The order in which the balls are selected does not matter. What is the probability of winning this lottery with one ticket?

An urn has 8 red and 12 blue balls. Suppose that balls are chosen at random...

An urn has 8 red and 12 blue balls. Suppose that balls are chosen at random and removed from the urn, with the process stopping when all the red balls have been removed. Let X be the number of balls that have been removed when the process stops. a. Find P(X = 14) b. Find the probability that a specifed blue ball remains in the urn. c. Find E[X]

An urn contains six white balls and four black balls. Two balls are randomly selected from...

An urn contains six white balls and four black balls. Two balls are randomly selected from the urn. Let X represent the number of black balls selected. (a) Identify the probability distribution of X. State the values of the parameters corresponding to this distribution. (b) Compute P(X = 0), P(X = 1), and P(X = 2). (c) Consider a game of chance where you randomly select two balls from the urn. You then win $2 for every black ball selected...

Suppose that there is a white urn containing two white balls and three red balls and...

Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red.

3. An urn contains 12 red balls and 8 green balls. Six balls are drawn randomly...

3. An urn contains 12 red balls and 8 green balls. Six balls are drawn randomly with replacement a. Find the probability of drawing exactly two red balls? b. Find the probability of drawing at least one green ball? c. Find the probability of drawing exactly two green balls when the drawings are done without replacement?

An urn contains 4 red balls and 3 green balls. Two balls are sampled randomly. Let...

An urn contains 4 red balls and 3 green balls. Two balls are sampled randomly. Let W denote the number of green balls in the sample when the draws are done with replacement. Give the possible values and the PMF of W.

Suppose that a subset of 4 balls will be randomly selected and removed from an urn...

Suppose that a subset of 4 balls will be randomly selected and removed from an urn initially containing 6 blue balls and 6 green balls, and then another subset of 4 balls will be randomly selected and removed from the 8 balls that remain (after the first subset of 4 balls is removed). Letting X be the number of these subsets that contain more blue balls than green balls, give the value of E(X). (Note: This problem may be solved...